Control-oriented models of channel flow

This talk addresses low-dimensional models of the transitional flow through a plane channel. Recent improvements to the technique of proper orthogonal decomposition (POD) and Galerkin projection are reviewed, including the use of carefully-chosen inner products, and the relation of POD/Galerkin to balanced truncation, a method commonly used for linear systems. The method naturally incorporates control inputs, and when applied to a linearized plane channel flow with streamwise-constant perturbations, reduced-order models obtained from balanced truncation produce an order of magnitude smaller error in the $H_\infty$ norm, compared to the standard POD procedure using the same number of modes.